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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A family of Monge-Ampère type operators converging to sigma_k, and their Minkowski problems
sigma_k汇聚 蒙日安培型 算子家族 闵可夫斯基问题
2023/4/17
We introduced a new family of translation invariant geometric measures arising from Integral Geometry of convex bodies. These measures are related to a family of new Monge-Ampère type operators conver...
GIAMBELLI, PIERI, AND TABLEAU FORMULAS VIA RAISING OPERATORS
GIAMBELLI PIERI TABLEAU FORMULAS
2015/12/17
We give a direct proof of the equivalence between the Giambelli
and Pieri type formulas for Hall-Littlewood functions using Young’s raising operators, parallel to joint work with Buch and Kresch for ...
We develop methods for studying transition operators on metric
spaces that are invariant under a co-compact group which acts properly.
A basic requirement is a decomposition of such operators with
...
FIRST EIGENVALUES OF GEOMETRIC OPERATORS UNDER THE RICCI FLOW
GEOMETRIC OPERATORS UNDER FLOW
2015/8/17
In this paper, we prove that the first eigenvalues of
−∆ + cR (c ≥
1
4
) is nondecreasing under the Ricci flow. We also
prove the monotonicity under the normalized Ricci &...
We show that elements of a natural basis of the Iwahori xed vectors in a principal series representation of a reductive p-adic group
satisfy certain recursive relations. The precise identities invol...
Fast Computation of Fourier Integral Operators
Fourier integral operators generalized Radon transform separated representation nonuniform fast Fourier transform matrix approximation operator compression randomized algorithms reflection seismology
2015/6/17
We introduce a general purpose algorithm for rapidly computing certain types of oscillatory integrals which frequently arise in problems connected to wave propagation and general hyperbolic equations....
A Fast Butterfly Algorithm for the Computation of Fourier Integral Operators
Fourier integral operators the butterfly algorithm dyadic partitioning Lagrange interpolation separated representation multiscale computations
2015/6/17
This paper is concerned with the fast computation of Fourier integral operators of the general form RRd e2πıΦ(x,k)f(k)dk, where k is a frequency variable, Φ(x, k) is a phase function obeying a st...
A Note on Gluing Dirac Type Operators on a Mirror Quantum Two-Sphere
Gluing Dirac Type Operators Mirror Quantum Two-Sphere
2014/12/12
The goal of this paper is to introduce a class of operators, which we call quantum Dirac type operators on a noncommutative sphere, by a gluing construction from copies of noncommutative disks, subjec...
Nullspaces of Conformally Invariant Operators. Applications to $Q_{k}$-curvature
Spectral geometry conformal geometry nodal sets Qk-curvature
2012/6/19
We study conformal invariants that arise from functions in the nullspace of conformally covariant differential operators. The invariants include nodal sets and the topology of nodal domains of eigenfu...
Integral estimates for the trace of symmetric operators on complete submanifolds
Integral estimates trace of symmetric operators complete submanifolds Differential Geometry
2012/4/17
Let $\Phi:TM\to TM$ be a positive-semidefinite operator of class $C^1$ defined on a complete noncompact manifold $M$ isometrically immersed in a Hadamard space $\bar{M}$. In this paper, we given condi...
Logarithmic tensor category theory, VI: Expansion condition, associativity of logarithmic intertwining operators, and the associativity isomorphisms
Logarithmic tensor category theory, VI: Expansion condition associativity of logarithmic intertwining operators associativity isomorphisms
2011/2/23
This is the sixth part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (...
Logarithmic tensor category theory, II: Logarithmic formal calculus and properties of logarithmic intertwining operators
Logarithmic tensor category theory Logarithmic formal calculus properties of logarithmic intertwining operators
2011/2/23
This is the second part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper ...
On the numerical radius of operators in Lebesgue spaces
the numerical radius Lebesgue spaces
2010/11/24
We show that the absolute numerical index of the space $L_p(\mu)$ is $p^{-1/p} q^{-1/q}$ (where $1/p+1/q=1$). In other words, we prove that $$ \sup\{\int |x|^{p-1}|Tx|\, d\mu \, : \ x\in L_p(\mu),\,\|...
A Borg-Levinson theorem for higher order elliptic operators
A Borg-Levinson theorem elliptic operators
2010/11/15
We establish the Borg-Levinson theorem for elliptic operators of higher order with constant coefficients. The case of incomplete spectral data is also considered.
Three-Colorings of Cubic Graphs and Tensor Operators
3-colorings of cubic planar graphs tensor algebras
2010/12/6
Penrose’s work [6] established a connection between the edge 3-colorings of cubic planar graphs and tensor algebras. We exploit this point of view in order to get algebraic representations of the cate...